arXiv subjects

Ylann Rouzaire

Publications and source records attributed to Ylann Rouzaire.

6 recordsLinked to original sources

arXiv2026

Topological defects in out-of-equilibrium systems

In this PhD thesis, we study topological defects in two-dimensional non-equilibrium systems, focusing on active extensions of the XY model, including activity, mobility and non-reciprocity. In a noisy Kuramoto lattice with short-range coupling, intrinsic frequency heterogeneity destroys quasi-long-range order and fragments the system into finite domains. Defects unbind at all temperatures and exhibit superdiffusive random walks, advected by evolving domain boundaries. By contrast, when oscillators are allowed to move in space, the system undergoes a Berezinskii-Kosterlitz-Thouless transition and regains quasi-long-range order, revealing the fundamental role of motility in sustaining coherence. We also analyse a non-reciprocal O(2) model with vision-cone couplings and derive a continuum theory that captures the same large-scale physics. Non-reciprocity selects defect shapes, enriches the annihilation process, and reshapes patterns through advection. Together, these results elucidate the fundamental role of activity and non-reciprocity in shaping topological defects and ordering in non-equilibrium systems. Keywords: Topological defects, XY model, Steep XY model, Kuramoto model, Non-reciprocal interactions, Active matter, Phase transitions, Berezinskii-Kosterlitz-Thouless transition, Non-equilibrium statistical mechanics

cond-mat.stat-mech↗

arXiv2026

Dynamics of O(2) excitations in a non-reciprocal medium

We investigate emergent dynamics due to non-reciprocity in the $\mathcal{O}(2)$ model. The lattice XY model, where non-reciprocity stems from vision cone like couplings, can be described by a continuum description in which non-reciprocity translates into a new term depending on the rotational of the orientation field. We argue that non-reciprocity is akin to activity and we highlight the connection between our hydrodynamic equation and the constant density Toner-Tu framework. The active force advects and reshapes patterns, a generic feature found in many non-reciprocal systems. We show how $1d$ excitations in the non-reciprocal $\mathcal{O}(2)$ model can be described by a generalized Burgers equation, derived from our continuum model. We then extend the results to $2d$ perturbations. As such, we establish the first principles of excitation trajectory control in a non-reciprocal $\mathcal{O}(2)$ medium. Concretely, we explain how tuning the degree of non-reciprocity and the orientation of the background medium impacts the time evolution of excitations. We also showcase how initially different excitations lead to very different dynamical behavior. Non-reciprocity also affects the stability of defect-free excitations with non-zero winding numbers and, unlike in its equilibrium $O(2)$ counterpart, enables the system, above a certain threshold, to relax to its ground state.

cond-mat.stat-mech↗

arXiv2025

Activity leads to topological phase transition in 2D populations of heterogeneous oscillators

Populations of heterogeneous, noisy oscillators on a two-dimensional lattice display short-range order. Here, we show that if the oscillators are allowed to actively move in space, the system undergoes instead a Berezenskii-Kosterlitz-Thouless transition and exhibits quasi-long-range order. This fundamental result connects two paradigmatic models -- XY and Kuramoto model -- and provides insight on the emergence of order in active systems.

cond-mat.stat-mech↗

arXiv2025

Non-Reciprocal Interactions Reshape Topological Defect Annihilation

We show how non-reciprocal ferromagnetic interactions between neighbouring planar spins in two dimensions, affect the behaviour of topological defects. Non-reciprocity is introduced by weighting the coupling strength of the two-dimensional XY model by an anisotropic kernel. As a consequence, in addition to the topological charge $q$, the actual shape of the defects becomes crucial to faithfully describe their dynamics. Non-reciprocal coupling twists the spin field, selecting specific defect shapes, dramatically altering the pair annihilation process. Defect annihilation can either be enhanced or hindered, depending on the shape of the defects concerned and the degree of non-reciprocity in the system. We introduce a continuous description -- for which the phenomenological coefficients can be explicitly written in terms of the microscopic ones -- that captures the behaviour of the lattice model.

cond-mat.stat-mech↗

arXiv2022

Dynamics of Topological Defects in the noisy Kuramoto Model in two dimensions

We consider the two-dimensional (2D) noisy Kuramoto model of synchronization with short-range coupling and a Gaussian distribution of intrinsic frequencies, and investigate its ordering dynamics following a quench. We consider both underdamped (inertial) and over-damped dynamics, and show that the long-term properties of this intrinsically out-of-equilibrium system do not depend on the inertia of individual oscillators. The model does not exhibit any phase transition as its correlation length remains finite, scaling as the inverse of the standard deviation of the distribution of intrinsic frequencies. The quench dynamics proceeds via domain growth, with a characteristic length that initially follows the growth law of the 2D XY model, although is not given by the mean separation between defects. Topological defects are generically free, breaking the Berezinskii-Kosterlitz-Thouless scenario of the 2D XY model. Vortices perform a random walk reminiscent of the self-avoiding random walk, advected by the dynamic network of boundaries between synchronised domains; featuring long-time super-diffusion, with the anomalous exponent $α=3/2$.

cond-mat.stat-mech↗

arXiv2021

Defects Superdiffusion and Unbinding in a 2D XY Model of Self-Driven Rotors

We consider a non-equilibrium extension of the two-dimensional (2D) XY model, equivalent to the noisy Kuramoto model of synchronization with short-range coupling, where rotors sitting on a square lattice are self-driven by random intrinsic frequencies. We study the static and dynamic properties of topological defects (vortices) and establish how self-spinning affects the Berezenskii-Kosterlitz-Thouless phase transition scenario. The non-equilibrium drive breaks the quasi-long-range ordered phase of the 2D XY model into a mosaic of ordered domains of controllable size and results in self-propelled vortices that generically unbind at any temperature, featuring superdiffusion $\langle r^2(t)\rangle\sim t^{3/2}$ with a Gaussian distribution of displacements. Our work provides a simple framework to investigate topological defects in active matter and sheds new light on the problem of synchronization of locally coupled oscillators.

cond-mat.stat-mech↗